Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

In an L-R-C series circuit, R = 400 Ω, L = 0.350 H, and C = 0.0120 mF. (a) What is the resonance angular frequency of the circuit? (b) The capacitor can withstand a peak voltage of 670 V. If the voltage source operates at the resonance frequency, what maximum voltage amplitude can it have if the maximum capacitor voltage is not exceeded?

Short Answer

Expert verified

(a)The resonance angular frequency of the circuit is and (b) Maximum voltage amplitude it can have if the maximum capacitor voltage is not exceeded is 40.7V.

Step by step solution

01

Step-1: Formulas used  

The angular frequency depends on the inductance and the capacitance and it is given by ω=1LC.

Capacitive reactance is given byXC=1ωC

02

Step-2: Calculation of angular frequency

When the angular frequency is varied, the current amplitude will change and the maximum current is produced at the minimum impedance. The process of peaking the current represents the resonance where the initial angular frequency is the same for the final angular frequency.

Plug the values of L and C into equation

ω=1LC=10.350H0.0120×10-6F=1.54×104rad/s

03

Step-3: (b)Calculation of maximum voltage amplitude

First calculate the capacitive reactance

XC=11.54×104rad/s0.0120×10-6F=5410Ω

The current through the capacitor is given by

I=VcXc=550V5410Ω=0.101A

Now, get the amplitude voltage by

V=0.101A400Ω=40.7V

Hence, (a)The resonance angular frequency of the circuit isω=1.54×104rad/s and (b) Maximum voltage amplitude it can have if the maximum capacitor voltage is not exceeded is 40.7V.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An 18-gauge copper wire (diameter 1.02 mm) carries a current

with a current density of 3.2×106Am2. The density of free electrons for

copper is8.5×1028electrons per cubic meter. Calculate (a) the current in

the wire and (b) the drift velocity of electrons in the wire.

Two copper wires with different diameter are joined end to end. If a current flow in the wire combination, what happens to electrons when they move from the large diameter wire into the smaller diameter wire? Does their drift speed increase, decrease, or stay the same? If the drift speed change, what is the role the force that causes the change? Explain your reasoning.

A battery-powered global positioning system (GPS) receiver operating 9.0 V on draws a current of 0.13 A. How much electrical energy does it consume during 30 minutes?

Electrons in an electric circuit pass through a resistor. The wire on either side of the resistor has the same diameter.(a) How does the drift speed of the electrons before entering the resistor compare to the speed after leaving the resistor? (b) How does the potential energy for an electron before entering the resistor compare to the potential energy after leaving the resistor? Explain your reasoning.

Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ωand 800Ω. If the two light bulbs are connected in series across a 120Vline, find (a) the current through each bulb; (b) the power dissipated in each bulb; (c) the total power dissipated in both bulbs. The two light bulbs are now connected in parallel across the120Vline. Find (d) the current through each bulb; (e) the power dissipated in each bulb; (f) the total power dissipated in both bulbs. (g) In each situation, which of the two bulbs glows the brightest? (h) In which situation is there a greater total light output from both bulbs combined?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free